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Introduction to information theory and data compression Second Edition 信息论与数据压缩，经典书籍 Darrel Hankerson Greg A. Harris Peter D. Johnson, Jr.

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© 2003 by CRC Press LLC

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and

DISCRETE

MATHEMATICS

ITS APPLICATIONS

© 2003 by CRC Press LLC

CHAPMAN & HALL/CRC

A CRC Press Company

Boca Raton London New York Washington, D.C.

Darrel Hankerson

Greg A. Harris

Peter D. Johnson, Jr.

Information

Theory

and

Data

Compression

Introduction to

Second Edition

© 2003 by CRC Press LLC

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with

permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish

reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials

or for the consequences of their use.

Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical,

including photocopying, microﬁlming, and recording, or by any information storage or retrieval system, without prior

permission in writing from the publisher.

The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works,

or for resale. Speciﬁc permission must be obtained in writing from CRC Press LLC for such copying.

Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.

Trademark Notice:

Product or corporate names may be trademarks or registered trademarks, and are used only for

identiﬁcation and explanation, without intent to infringe.

Visit the CRC Press Web site at www.crcpress.com

© 2003 by CRC Press LLC

No claim to original U.S. Government works

International Standard Book Number 1-58488-313-8

Library of Congress Card Number 2002041506

Printed in the United States of America 1 2 3 4 5 6 7 8 9 0

Printed on acid-free paper

Library of Congress Cataloging-in-Publication Data

Hankerson, Darrel R.

Introduction to information theory and data compression / Darrel R. Hankerson, Greg A.

Harris, Peter D. Johnson.--2nd ed.

p. cm. (Discrete mathematics and its applications)

Includes bibliographical references and index.

ISBN 1-58488-313-8 (alk. paper)

1. Information theory. 2. Data compression (Computer science) I. Harris, Greg A. II.

Johnson, Peter D. (Peter Dexter), 1945- III. Title. IV. Series.

Q360.H35 2003

005.74

¢6

—dc21 2002041506

CIP

C3138-discl. Page 1 Friday, January 17, 2003 1:19 PM

© 2003 by CRC Press LLC

Preface

This textbook is aimed at graduate students and upper level undergraduates

in mathematics, engineering, and computer science. The material and the ap-

proach of the text were developed over several years at Auburn University in two

independent courses, Information Theory and Data Compression. Although the

material in the two courses is related, we think it unwise for information theory

to be a prerequisite for data compression, and have written the data compression

section of the text so that it can be read by or presentedtostudents with no prior

knowledge of information theory. There are references in the data compression

part to results and proofs in the information theory part of the text, and those

who are interested may browse over those references, but it is not absolu tely

necessary to do so. In fact, perhaps the best pedagogical order of approach to

these subjects is the reverseoftheapparent logical order: students will come

to information theory curious an d bette rprepared for having seen some of the

deﬁnitions and theorems of that subject playing a role in data compression.

Our main aim in the data compression part of the text, as well as in the

course it grew from, is to acquaint the students with a number of signiﬁcant

lossless compression techniques, and to discuss two lossy compression meth-

ods. Our aim is for the students to emerge competent in and broadly conversant

with a large range of techniques. We have striven for a “practical” style of

presentation: here is what you do and here is what it is good for. Nonethe-

less, proofs are provided, sometimes in the text, sometimes in the exercises, so

that the instructor can have the option of emphasizing the mathematics of data

compression to some degree.

Information theory is of a more theoretical nature than data compression.

It provides a vocabulary and a certain abstraction that can bring the power of

simpliﬁcation to many different situations. We thought it reasonable to treat it

as a mathematical theory and to present the fundamental deﬁnitions and ele-

mentary results of that theory in utter abstraction from the particular problems

of communication through noisy channels, which inspired the theory in the ﬁrst

place. We bring the theory to bear on noisy channels in Chapters 3 and 4.

The treatment of information theory given here is extremely elementary.

The channels are memoryless and discrete, and the sources are all “zeroth-

order,” one-state sources (although more complicated source models are dis-

cussed in Chapter 7). We feel that this elementary approach is appropriate for

the target audience, and that, by leavingmorecomplicated sources and channels

out of the picture, we more effectively impart the grasp of Information Theory

that we hope our students will take with them.

The exercises range from the routine to somewhat lengthy problems that

introduce additional material or establish more difﬁcult results. An asterisk by

v

© 2003 by CRC Press LLC

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